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A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. , the value of the function's midpoint; , the supremum of the values of the function; , the logistic growth rate or steepness of the curve. [1] Standard logistic function where. For values of in the domain of real numbers from to , the S ...
And some functions, such as the logistic function, approximate exponential growth over only part of their range. The "technical details" section below explains exactly what is required for a function to exhibit true exponential growth. But the general principle behind exponential growth is that the larger a number gets, the faster it grows.
Berezin integral. In mathematical physics, the Berezin integral, named after Felix Berezin, (also known as Grassmann integral, after Hermann Grassmann ), is a way to define integration for functions of Grassmann variables (elements of the exterior algebra ). It is not an integral in the Lebesgue sense; the word "integral" is used because the ...
The growth function, also called the shatter coefficient or the shattering number, measures the richness of a set family or class of function. It is especially used in the context of statistical learning theory, where it is used to study properties of statistical learning methods. The term 'growth function' was coined by Vapnik and Chervonenkis ...
The Riemann zeta function ζ(s) is a function of a complex variable s = σ + it, where σ and t are real numbers. (The notation s, σ, and t is used traditionally in the study of the zeta function, following Riemann.) When Re (s) = σ > 1, the function can be written as a converging summation or as an integral: where.
The simplest non-trivial examples are the exponential growth model/decay (one unstable/stable equilibrium) and the logistic growth model (two equilibria, one stable, one unstable). The phase space of a two-dimensional system is called a phase plane , which occurs in classical mechanics for a single particle moving in one dimension, and where ...
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